Pulbtent
(9)
In a two-dimansional vectors spere. Conster the operator whace maletis, in on orthencrmal bapis \( \{14>, 12>\} \), is werithen.
\[
\sigma_{y}=\left(\begin{array}{cc}
0 & -i \\
1 & 0
\end{array}\right)
\]
Q. is 6 y Hermition? Calculate its eigonvabaes and eifenvectors ( giving their noumized expension in terms of the \( \{|1\rangle,|2\rangle\} \) basis).
b) Calculate the matrices which represent The projectors orto these eigenvectors. Frea rewify that they satisfy the orthogavily and Closure relations.
c. Same question for the matrices:
\[
M=\left(\begin{array}{cc}
2 & i \sqrt{2} \\
-1 \sqrt{2} & 3
\end{array}\right)
\]
onds, in a thice - dirmensional space
\[
L_{y}=\frac{h}{21}\left[\begin{array}{ccc}
0 & \sqrt{2} & 0 \\
-\sqrt{3} & 0 & \sqrt{2} \\
0 & -\sqrt{2} & 0
\end{array}\right)
\]
